Question

you are given a positive integer n n. let s ( x ) s(x) be sum of digits in base 10 representation of x x, for example, s ( 123 ) = 1 + 2 + 3 = 6 s(123)=1+2+3=6, s ( 0 ) = 0 s(0)=0. your task is to find two integers a , b a,b, such that 0 ≤ a , b ≤ n 0≤a,b≤n, a + b = n a+b=n and s ( a ) + s ( b ) s(a)+s(b) is the largest possible among all such pairs

Answer 1

If the last digit of this positive number becomes the first digit, the resulting number is exactly twice as large. My number is the smallest positive number with this property. What is my number? (Clarification: by “number” I mean a whole number or positive integer).

You might be able to find some numbers that almost work.

25 would become 52, which is close to 25(2) = 50

102 would become 210, which is close to 102(2) = 204

What is my number?

I’ll give you a hint: you are unlikely to solve for the answer by casually guessing it.

But a genius might be able to. Legendary mathematician Freeman Dyson apparently heard the problem and instantly replied with the number of digits in the answer